Portal:Mathematics
The Mathematics Portal
Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
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- ... that Ukrainian baritone Danylo Matviienko, who holds a master's degree in mathematics, appeared as Demetrius in Britten's opera A Midsummer Night's Dream at the Oper Frankfurt?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that museum director Alena Aladava rebuilt the Belarusian national art collection in the aftermath of the Second World War?
- ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
- ... that subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
- ... that The Math Myth advocates for American high schools to stop requiring advanced algebra?
- ... that in the aftermath of the American Civil War, the only Black-led organization providing teachers to formerly enslaved people was the African Civilization Society?
- ... that Latvian-Soviet artist Karlis Johansons exhibited a skeletal tensegrity form of the Schönhardt polyhedron seven years before Erich Schönhardt's 1928 paper on its mathematics?
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- ...that Ostomachion is a mathematical treatise attributed to Archimedes on a 14-piece tiling puzzle similar to tangram?
- ...that some functions can be written as an infinite sum of trigonometric polynomials and that this sum is called the Fourier series of that function?
- ...that the identity elements for arithmetic operations make use of the only two whole numbers that are neither composites nor prime numbers, 0 and 1?
- ...that as of April 2010 only 35 even numbers have been found that are not the sum of two primes which are each in a Twin Primes pair? ref
- ...the Piphilology record (memorizing digits of Pi) is 70000 as of Mar 2015?
- ...that people are significantly slower to identify the parity of zero than other whole numbers, regardless of age, language spoken, or whether the symbol or word for zero is used?
- ...that Auction theory was successfully used in 1994 to sell FCC airwave spectrum, in a financial application of game theory?
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Fractals arise in surprising places, in this case, the famous Collatz conjecture in number theory. Image credit: Pokipsy76 |
A fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole". The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured".
A fractal as a geometric object generally has the following features:
- It has a fine structure at arbitrarily small scales.
- It is too irregular to be easily described in traditional Euclidean geometric language.
- It is self-similar (at least approximately or stochastically).
- It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
- It has a simple and recursive definition.
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics. Fractals, when zoomed in, will keep showing more and more of itself, and it keeps going for infinity. (Full article...)
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